An algorithm to generate all spanning trees with flow

Spanning tree enumeration in undirected graphs is an important issue and task in many problems encountered in computer network and circuit analysis. This paper discusses the spanning tree with flow for the case that there are flow requirements between each node pair. An algorithm based on minimal paths (MPs) is proposed to generate all spanning trees without flow. The proposed algorithm is a structured approach, which splits the system into structural MPs first, and also all steps in it are easy to follow.